For the following equations, write a word problem draw a picture, and find the solution to the equation:
5/12 - 1/3=
1/2 - 2/3=
To write a word problem for each equation, we need to come up with a scenario where the fractions represent different quantities or parts of a whole. Let's see:
Equation 1: 5/12 - 1/3 =
Word Problem 1: Ella had a pizza with 12 slices. She ate 5 slices, and her friend Logan ate 1/3 of the pizza. How many slices did Ella have left?
Picture 1: Draw a circle to represent the pizza with lines dividing it into 12 equal slices. Shade 5 of the slices to represent the slices Ella ate. Then, divide one-third of the pizza into three equal parts and shade one of those parts to represent the slices Logan ate.
Solution 1: To find the solution, we subtract the fraction Logan ate (1/3) from the fraction Ella ate (5/12).
To subtract fractions, we need the same denominator. So, let's rewrite 1/3 with a denominator of 12: 4/12.
Now, we can subtract: 5/12 - 4/12 = 1/12.
Therefore, Ella had 1/12 of the pizza left.
Equation 2: 1/2 - 2/3 =
Word Problem 2: Sarah bought a cake with 6 equal slices. She ate half of the cake, and her sister Maria ate 2/3 of what was left. How much of the cake does Sarah have left?
Picture 2: Draw a rectangle to represent the cake and divide it into 6 equal slices. Shade 3 of the slices to represent the slices Sarah ate. Then, divide the remaining half of the cake into three equal parts and shade two of those parts to represent the slices Maria ate.
Solution 2: To find the solution, we subtract the fraction Maria ate (2/3) from the fraction Sarah ate (1/2).
To subtract fractions, we need the same denominator. So, let's rewrite 1/2 with a denominator of 6: 3/6.
Now, we can subtract: 3/6 - 2/6 = 1/6.
Therefore, Sarah has 1/6 of the cake left.
Note: Make sure to simplify the fractions in the solutions and represent them in the simplest form.